Q52. - Algebra 2

Question

Use the table that shows the years of experience for eight sales representative and their sales during a given period of time.

years	6	5	3	1	4	3	6	2
Sales	9000	6000	4000	3000	6000	5000	8000	2000

Find the prediction equation

Step-by-Step Solution

Answer

The prediction equation is $y=\frac{4}{7000}x+\frac{6}{7}$.

Step 1 : Identify two points representative for best fit line

The slope is 

$\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{6-2}{9000-2000}\\ m=\frac{4}{7000}\end{array}$

Step 2 : Substitutes on of the points

Substation of the point in the above equation 

$\begin{array}{l}y=mx+c\\ y=\frac{4}{7000}x+b\end{array}$

Step 3 : Solve for b for complete prediction

X=9000

Y=6

$\begin{array}{l}6=\frac{4}{7000}9000+b\\ b=\frac{6}{7}\end{array}$

On substituting the value of b 

$y=\frac{4}{7000}x+\frac{6}{7}$

Hence, the final inequalities is   $\frac{4}{7000}x+\frac{6}{7}$.